\subsubsection*{Evaluation by Simulation}

As in Section \ref{analysisofsolutions:nonexpandingwindows} the analytical expressions for the decoding probabilities, derived in Equation \eqref{eq:ew_l1_anal} for \ac{L1} and in \eqref{eq:ew_l2_anal} for \ac{L2}, is evaluated by means of a simulation. The evaluation is done under the same premises as the one given in Section \ref{analysisofsolutions:nonexpandingwindows}. The resulting difference graphs are shown in Figure \ref{fig:diff_plot_ew_l1} and \ref{fig:diff_plot_ew_l2}. The source code and data output for the simulation is available on the Project DVD \cite{cd}.

\begin{figure}[h]
\centering
\includegraphics[width=1\textwidth]{figs/l1_ew_dif.eps}
\caption{Difference between the simulated and analytical decoding probabilities for L1 using EW UEP, given in percentage points ([pp]).}
\label{fig:diff_plot_ew_l1}
\end{figure}


\begin{figure}[h]
\centering
\includegraphics[width=1\textwidth]{figs/l2_ew_dif.eps}
\caption{Difference between the simulated and analytical decoding probabilities for L2 using EW UEP, given in percentage points ([pp]).}
\label{fig:diff_plot_ew_l2}
\end{figure}

\newpage
The simulated and analytical probabilities shows a small difference. The peak deviation is $\approx 1.3$ percentage point on \ac{L1} with $\boldsymbol \Gamma_1=0.5$ as seen in Figure \ref{fig:diff_plot_ew_l1}. As in Section \ref{analysisofsolutions:nonexpandingwindows} the deviations seem of random nature and thereby considered noncritical. Also the argument explanation for the deviation applies to this comparison, thereby proving the validity of the analytical expressions.
